The striker, who turns 26 next week, has penned a three-and-a-half-year deal at St Mary's and joins for an undisclosed fee.
Sharp, who is reunited with his former manager at Scunthorpe, Nigel Adkins, told the club's official website: "I'm delighted. It has been a long time coming, but I am delighted to get it done, and now I am just looking forward to getting on the pitch and showing the fans what I can do.
"It's a massive club with huge ambitions, and that is the main reason. The gaffer and his coaching team was another reason and it felt right in my head too. I can't wait to get on with the challenge.
"I got on well with the fans at Doncaster and had an amazing time there and I'm gutted that I had to leave.
"That said, I am delighted that I am here and joining a really big club with a strong squad of players, hopefully I can be a cog in the team that helps get this huge club into the Premier League."